275 bytes
\.?([cmst][cdghk-orvz]|[agim][delmq-t]|[dft][jkmo]|[acms]x|[bcgkmp][ghmnrwy]|[psu][agksy]|[aen][cegru]|[abcn][fioz]|l[abcikr-vy]|[bdjkprsvy]e|[bcgmnqvz]a|[behpsty]t|[cghmrv]u|[fgksv]i|[gjkmn]p|b[bdjs]|h[kmnr]|[gptw]f|[artz]w|v[cgn]|[joz]m|[ijr]o|[erw]s|[dku]z|[np]l|fr|in|sb)
(277 bytes including ^$.) A Python program was used to autogenerate part of this regular expression. Here is the first version of the program:
def makeregex(list):
if len(list) == 1:
return alpha[list[0]]
regex = "["
j = list[0]
while j < 26:
if j in list:
if j + 1 in list and j + 2 in list and j + 3 in list:
regex += alpha[j] + "-"
while j + 1 in list:
j += 1
regex += alpha[j]
j += 1
return regex + "]"
def perform(rows, cols):
replaced = '|'.join([alpha[j] + alpha[k] for j in rows for k in cols if array[j][k] > 0])
regex = makeregex(rows) + makeregex(cols)
print regex, 'replaces', replaced, 'saving', len(replaced) - len(regex), 'bytes'
for j in rows:
for k in cols:
if (array[j][k]):
array[j][k] = -1
else:
raise Exception("filling illegal entry")
all = ['ac', 'ad', 'ae', 'af', 'ag', 'ai', 'al', 'am', 'ao', 'aq', 'ar', 'as',
'at', 'au', 'aw', 'ax', 'az', 'ba', 'bb', 'bd', 'be', 'bf', 'bg', 'bh',
'bi', 'bj', 'bm', 'bn', 'bo', 'br', 'bs', 'bt', 'bw', 'by', 'bz', 'ca',
'cc', 'cd', 'cf', 'cg', 'ch', 'ci', 'ck', 'cl', 'cm', 'cn', 'co', 'cr',
'cu', 'cv', 'cw', 'cx', 'cy', 'cz', 'de', 'dj', 'dk', 'dm', 'do', 'dz',
'ec', 'ee', 'eg', 'er', 'es', 'et', 'eu', 'fi', 'fj', 'fk', 'fm', 'fo',
'fr', 'ga', 'gd', 'ge', 'gf', 'gg', 'gh', 'gi', 'gl', 'gm', 'gn', 'gp',
'gq', 'gr', 'gs', 'gt', 'gu', 'gw', 'gy', 'hk', 'hm', 'hn', 'hr', 'ht',
'hu', 'id', 'ie', 'il', 'im', 'in', 'io', 'iq', 'ir', 'is', 'it', 'je',
'jm', 'jo', 'jp', 'ke', 'kg', 'kh', 'ki', 'km', 'kn', 'kp', 'kr', 'kw',
'ky', 'kz', 'la', 'lb', 'lc', 'li', 'lk', 'lr', 'ls', 'lt', 'lu', 'lv',
'ly', 'ma', 'mc', 'md', 'me', 'mg', 'mh', 'mk', 'ml', 'mm', 'mn', 'mo',
'mp', 'mq', 'mr', 'ms', 'mt', 'mu', 'mv', 'mw', 'mx', 'my', 'mz', 'na',
'nc', 'ne', 'nf', 'ng', 'ni', 'nl', 'no', 'np', 'nr', 'nu', 'nz', 'om',
'pa', 'pe', 'pf', 'pg', 'ph', 'pk', 'pl', 'pm', 'pn', 'pr', 'ps', 'pt',
'pw', 'py', 'qa', 're', 'ro', 'rs', 'ru', 'rw', 'sa', 'sb', 'sc', 'sd',
'se', 'sg', 'sh', 'si', 'sk', 'sl', 'sm', 'sn', 'so', 'sr', 'ss', 'st',
'sv', 'sx', 'sy', 'sz', 'tc', 'td', 'tf', 'tg', 'th', 'tj', 'tk', 'tl',
'tm', 'tn', 'to', 'tr', 'tt', 'tv', 'tw', 'tz', 'ua', 'ug', 'uk', 'us',
'uy', 'uz', 'va', 'vc', 've', 'vg', 'vi', 'vn', 'vu', 'wf', 'ws', 'ye',
'yt', 'za', 'zm', 'zw']
alpha = 'abcdefghijklmnopqrstuvwxyz'
array = [[alpha[i] + alpha[j] in all for j in range(26)] for i in range(26)]
#perform([2, 12, 18, 19], [2, 3, 6, 7, 10, 11, 12, 13, 14, 17, 21, 25])
#perform([0, 6, 8, 12], [3, 4, 11, 12, 16, 17, 18, 19])
#perform([3, 5, 19], [9, 10, 12, 14])
#perform([0, 2, 12, 18], [23])
while max(max(row) for row in array) > 0:
best = 0
i = 1
while i < 1 << 26:
row = [-1 for j in range(26)]
for j in range(26):
if (i & 1 << j):
for k in range(26):
if array[j][k] == 0:
row[k] = 0
elif array[j][k] == 1 and row[k]:
row[k] = max(row[k], 0) + 1
if max(row) < 1:
break;
if max(row) > 0:
total = 3 * sum(max(j, 0) for j in row)
if total > best:
rows = [j for j in range(26) if i & 1 << j]
cols = [j for j in range(26) if row[j] > 0]
total -= len(makeregex(rows)) + len(makeregex(cols)) + 1
if total > best:
best = total
bestrows = rows
bestcols = cols
i += 1
else:
i += i & -i
if best:
perform(bestrows, bestcols)
else:
print '|'.join([alpha[j] + alpha[k] for j in range(26) for k in range(26) if array[j][k] > 0])
break
This 282-byte regex results from its output:
\.?([bgmps][aeghmnrsty]|[cmst][cdghk-orvz]|[acn][cfgiloruz]|[agim][delmq-t]|[bck][ghimnrwyz]|[elm][cr-u]|[dft][jkmo]|[agpt][fltw]|[gnv][aegiu]|[lpu][aksy]|[gjkm][emp]|h[kmnrtu]|b[bdfjo]|r[eosuw]|[ls][biv]|[acms]x|[cmz][amw]|[dey]e|dz|eg|fi|fr|in|io|jo|np|om|qa|ug|uz|vc|vn|wf|ws|yt)
The program can also be seeded by adding calls to perform, so I tried seeding it with [cmst][cdghk-orvz]|[agim][delmq-t]|[dft][jkmo]|[acms]x but that just resulted in a rearranged regex. Obviously this wasn't good enough. The problem seemed to be that I was comparing the performance against a simple alternation. I therefore developed a slower but more accurate scoring function, which works by assuming that all of the remaining matches should be either x[yz] or [xy]z alternations, generating the largest alternations first, and compares the result with and without the trial regex.
def makeregex(list):
if len(list) == 1:
return alpha[list[0]]
regex = "["
j = list[0]
while j < 26:
if j in list:
if j + 1 in list and j + 2 in list and j + 3 in list:
regex += alpha[j] + "-"
while j + 1 in list:
j += 1
regex += alpha[j]
j += 1
return regex + "]"
def simple(array):
unused = [[j > 0 for j in row] for row in array]
regex = ""
while max(max(row) for row in unused):
rowcount = [sum(row) for row in unused]
colcount = [sum(col) for col in zip(*unused)]
if max(colcount) > max(rowcount):
colindex = colcount.index(max(colcount))
col = zip(*unused)[colindex]
regex += "|" + makeregex([j for j in range(26) if col[j]]) + alpha[colindex]
for j in range(26):
unused[j][colindex] = 0
else:
rowindex = rowcount.index(max(rowcount))
row = unused[rowindex]
regex += "|" + alpha[rowindex] + makeregex([j for j in range(26) if row[j]])
unused[rowindex] = [0 for j in range(26)]
return regex
def perform(rows, cols):
previous = simple(array)[1:].split('|')
for j in rows:
for k in cols:
if (array[j][k]):
array[j][k] = -1
else:
raise Exception("filling illegal entry")
regex = (makeregex(rows) + makeregex(cols) + simple(array)).split('|')
replaced = '|'.join(j for j in previous if not j in regex)
regex = '|'.join(j for j in regex if not j in previous)
print regex, 'replaces', replaced, 'saving', len(replaced) - len(regex), 'bytes'
all = ['ac', 'ad', 'ae', 'af', 'ag', 'ai', 'al', 'am', 'ao', 'aq', 'ar', 'as',
'at', 'au', 'aw', 'ax', 'az', 'ba', 'bb', 'bd', 'be', 'bf', 'bg', 'bh',
'bi', 'bj', 'bm', 'bn', 'bo', 'br', 'bs', 'bt', 'bw', 'by', 'bz', 'ca',
'cc', 'cd', 'cf', 'cg', 'ch', 'ci', 'ck', 'cl', 'cm', 'cn', 'co', 'cr',
'cu', 'cv', 'cw', 'cx', 'cy', 'cz', 'de', 'dj', 'dk', 'dm', 'do', 'dz',
'ec', 'ee', 'eg', 'er', 'es', 'et', 'eu', 'fi', 'fj', 'fk', 'fm', 'fo',
'fr', 'ga', 'gd', 'ge', 'gf', 'gg', 'gh', 'gi', 'gl', 'gm', 'gn', 'gp',
'gq', 'gr', 'gs', 'gt', 'gu', 'gw', 'gy', 'hk', 'hm', 'hn', 'hr', 'ht',
'hu', 'id', 'ie', 'il', 'im', 'in', 'io', 'iq', 'ir', 'is', 'it', 'je',
'jm', 'jo', 'jp', 'ke', 'kg', 'kh', 'ki', 'km', 'kn', 'kp', 'kr', 'kw',
'ky', 'kz', 'la', 'lb', 'lc', 'li', 'lk', 'lr', 'ls', 'lt', 'lu', 'lv',
'ly', 'ma', 'mc', 'md', 'me', 'mg', 'mh', 'mk', 'ml', 'mm', 'mn', 'mo',
'mp', 'mq', 'mr', 'ms', 'mt', 'mu', 'mv', 'mw', 'mx', 'my', 'mz', 'na',
'nc', 'ne', 'nf', 'ng', 'ni', 'nl', 'no', 'np', 'nr', 'nu', 'nz', 'om',
'pa', 'pe', 'pf', 'pg', 'ph', 'pk', 'pl', 'pm', 'pn', 'pr', 'ps', 'pt',
'pw', 'py', 'qa', 're', 'ro', 'rs', 'ru', 'rw', 'sa', 'sb', 'sc', 'sd',
'se', 'sg', 'sh', 'si', 'sk', 'sl', 'sm', 'sn', 'so', 'sr', 'ss', 'st',
'sv', 'sx', 'sy', 'sz', 'tc', 'td', 'tf', 'tg', 'th', 'tj', 'tk', 'tl',
'tm', 'tn', 'to', 'tr', 'tt', 'tv', 'tw', 'tz', 'ua', 'ug', 'uk', 'us',
'uy', 'uz', 'va', 'vc', 've', 'vg', 'vi', 'vn', 'vu', 'wf', 'ws', 'ye',
'yt', 'za', 'zm', 'zw']
alpha = 'abcdefghijklmnopqrstuvwxyz'
array = [[alpha[i] + alpha[j] in all for j in range(26)] for i in range(26)]
#perform([2, 12, 18, 19], [2, 3, 6, 7, 10, 11, 12, 13, 14, 17, 21, 25])
#perform([0, 6, 8, 12], [3, 4, 11, 12, 16, 17, 18, 19])
#perform([3, 5, 19], [9, 10, 12, 14])
#perform([0, 2, 12, 18], [23])
while max(max(row) for row in array) > 0:
best = simple(array)[1:]
bestrows = []
bestcols = []
i = 1
while i < 1 << 26:
row = [-1 for j in range(26)]
for j in range(26):
if (i & 1 << j):
for k in range(26):
if array[j][k] == 0:
row[k] = 0
elif array[j][k] == 1 and row[k]:
row[k] = max(row[k], 0) + 1
if max(row) < 1:
break;
if max(row) > 0:
rows = [j for j in range(26) if i & 1 << j]
cols = [j for j in range(26) if row[j] > 0]
unused = [row[:] for row in array]
for j in rows:
for k in cols:
unused[j][k] = 0
total = makeregex(rows) + makeregex(cols) + simple(unused)
if len(total) < len(best):
best = total
bestrows = rows
bestcols = cols
i += 1
else:
i += i & -i
if bestrows:
perform(bestrows, bestcols)
else:
print best
break
Now without seeding, this actually produces the worse 286-byte regex:
\.?([bgp][ae-hmnrstwy]|[cst][cdghk-orvz]|[nv][acegiu]|m[acdeghk-z]|a[c-gilmoq-uwxz]|k[eghimnprwyz]|l[abcikr-vy]|i[del-oq-t]|s[abeistxy]|c[afiuwxy]|e[cegr-u]|b[bdijoz]|d[ejkmoz]|f[ijkmor]|g[dilpqu]|h[kmnrtu]|n[floprz]|u[agksyz]|r[eosuw]|j[emop]|t[fjtw]|z[amw]|p[kl]|w[fs]|y[et]|om|qa|vn)
When seeded with [cmst][cdghk-orvz] (which I had independently discovered manually before writing the first program) this improves to this 282-byte regex, thus equalling the first program:
\.?([cmst][cdghk-orvz]|[bgmps][aeghmnrsty]|[ag][d-gilmq-uw]|[pt][fkltw]|[acs][cioxz]|[nv][acegiu]|k[eghimnprwyz]|l[abcikr-vy]|i[del-oq-t]|b[bdfijowz]|e[cegr-u]|d[ejkmoz]|f[ijkmor]|h[kmnrtu]|n[floprz]|u[agksyz]|c[afuwy]|m[pquwx]|r[eosuw]|j[emop]|z[amw]|w[fs]|y[et]|gp|om|qa|sb|tj|vn)
After some experimentation I discovered that when seeded with [cmst][cdghk-orvz]|[agim][delmq-t]|[dft][jkmo]|[acms]x (selected from the output of the first version), it results in the given 275-byte regex.
For completeness, I think the best I achieved manually was the following 282-byte regex:
\.?(a[c-gilmoq-uwxz]|b[abd-jostz]|c[afiuwxy]|d[ejkmoz]|e[cegr-u]|f[ijkmor]|g[ad-ilp-u]|h[kmnrtu]|i[del-oq-t]|j[emop]|k[ipz]|l[abcikr-vy]|m[aep-y]|n[acefgilopruz]|om|p[aflst]|qa|r[eosuw]|s[abeistxy]|t[fjtw]|u[agksyz]|v[aceginu]|w[fs]|y[et]|z[amw]|[cmst][cdghk-orvz]|[bgkp][eghmnrwy])
